Structural and spectroscopic characteristics of Pyrromethene 567

laser dye. A theoretical approach

Jorge Banuelos Prieto, Fernando Lopez Arbeloa,* Virginia Martınez Martınez,

Teresa Arbeloa Lopez and Inigo Lopez Arbeloa

Departamento de Quımica Fısica, Universidad del Paıs Vasco-EHU, Apartado 644,48080-Bilbao, Spain. E-mail: qfploarf@lg.ehu.es; Fax: þ34 94 601 35 00;Tel: þ34 94 601 59 71

Received 26th April 2004, Accepted 18th May 2004First published as an Advance Article on the web 5th July 2004

Quantum mechanic calculations at the DFT (B3LYP) and semiempirical PM5 levels were performed to study thestructural and electronic properties of Pyrromethene 567 laser dye. TD-DFT and semiempirical ZINDO andCISD methods were carried out to predict the photophysical characteristics of the dye. The effect of the solventwas evaluated by means of SCRF (PCM) and the semiempirical COSMO models in c-hexane, acetone andmethanol, and the results are compared to the experimental data. Both algorithms indicate an increase of thecharge separation through the chromophore p-system in the polar solvents. This result explains the increase inthe dipole moment and the hypsochromic shift of the absorption and fluorescence spectral bands in polarsolvents, which is also experimentally observed, inducing a diminution in the dipole transition moment.

Introduction

Pyrromethenes are a family of laser dyes synthesized by Boyeret al. by means of the fluoroboration of two pyrrole ringslinked by a methylene group.1,2 These dyes have found wideapplications in a great variety of fields such as science, medi-cine, industry and technology due to their excellent photophy-sical and lasing characteristics. Pyrromethene (PM) dyes havestrong absorption and fluorescence bands covering the green-yellow and red region, with a high fluorescence quantumyield.3–5 As a consequence of this emission efficiency and dueto the low intersystem crossing probability,6,7 high lasing gainshave been achieved for PM dyes.8–11 Indeed, PM dyes can lasemore efficiently than rhodamine laser dyes, the most used laserdye family, due to the low triplet-triplet absorption in theformer dyes, which is one fifth of that of rhodamines.12 More-over, PM dyes yield higher photostabilities than rhodamines,although the presence of heteroaromatic nitrogen atoms makesthem sensitive to oxygen degradation.13–15

In a series of previous papers, the photophysics of severalPM dyes (commercially available and synthesized analogs) in amultitude of solvents from apolar to polar and protic solventshave been experimentally studied.4,16–18 These studies suggestthat the photophysical properties of PM dyes depend on themolecular structure and on the nature of the solvent. Alkylsubstituents at different positions of the chromophore p-systeminduce moderate changes in the photophysics of PM dyes. Theabsorption and fluorescence bands of alkyl-PM derivativesshift to higher energies in polar-protic solvents and thefluorescence quantum yield and lifetime increase in polarmedia.4,16–18 This augmentation is due to a diminution in thenon-radiative deactivation processes, concretely to the internalconversion, since the intersystem crossing of PM dyes is verylow.6,7 The internal conversion process is not fully understood,although it has been main related to the rigidity/flexibility ofthe molecular structure of PM chromophore.2,19

In order to obtain a deeper knowledge on the photophysicsof PM dyes, quantum mechanic calculations are now beingapplied to study the geometry and electronic properties ofthe PM chromophore. Recently we have demonstrated that the

geometrical parameters of PM546 dye (with methyl substitu-ents at the 1, 3, 5, 7 and 8 positions, Fig. 1), calculated by theDFT method, perfectly correlate with the experimental dataobtained by X-ray diffraction, although semiempirical AM1and mainly PM5 methods also satisfactorily reproduce thegeometry of PM546.20 Moreover, in this study was shown thatthe optimized geometry of the unsubstituted PM chromophorehas a planar C2v symmetry point group and that the presenceof methyl groups at 1, 3, 5 and 7 positions do not disturb theplanar structure of the chromophore, although the C2v sym-metry group was disrupted due to a non-symmetrical distribu-tion of the CH3 groups. The additional presence of a methylgroup at the 8 position (to render the commercial PM546 dye)slightly distorted the planarity of the central ring linking thetwo pyrrole rings, although these aromatic rings were notaffected by the presence of the methyl group at the 8 position.In the present paper quantum mechanical calculations at

DFT and semiempirical levels are performed for PM567(Fig. 1), probably the best-known PM dye. The theoreticalcalculations were focused on the evolution of the geometricalparameters, the electronic properties (dipole moment andcharge distribution) and the absorption and fluorescence char-acteristics of PM567 dye. The comparison of the present resultswith respect to those of PM546 previously obtained20 willallow the analysis of the effect of the presence of ethyl groupsat the 2 and 6 positions of the PM chromophore on theseproperties. Moreover, the theoretical calculations, at the selfconsistent reaction field (SCRF) and semiempirical conductor-like screening model (COSMO) levels of PM567, are extendedto study the effect of the solvent on the molecular geometry andphotophysical properties of PM567. Apolar (c-hexane), polar/non-protic (acetone) and polar/protic (methanol) solvents areconsidered for such a study, and the results are compared withthe experimentally observed evolution of the absorption andfluorescence characteristics in such media.17

Computational details

The optimization of the S0 ground state geometry of PM567 inthe gas phase is performed by the semiempirical PM5 method

R E S E A R C H P A P E R

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DOI:10.1039/b406269h

P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 2 4 7 – 4 2 5 3 4247T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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(implemented in the Mopac 200221 supplied in CAChe 5.0software) and by the density functional theory (DFT)method22 with the B3LYP functional23,24 (included in theGaussian 98 software).25 The basis sets used for DFT calcula-tions are the standard 6-31G and its polarization (6-31G*) anddiffuse (6-31þG*) functions. The PM5 method was chosen,against other semiempirical methods, due to its improvedcharacterization of the boron atom included in the structureof PM dyes.

The default options are considered for DFT optimizationsand, for the PM5 method, the eigenvector following (EF)routine setting the minimum gradient for convergence at0.01 kcal mol�1 A�1 was used. The optimization of the S0geometry was performed without any structural restriction anda frequency analysis was carried out to ensure that theobtained structure is an energy minimum.

The S0 state geometry of PM567 was also calculated takinginto account the solvent effect by means of the semiempiricalconductor-like screening model (COSMO) algorithm26 (incor-porated in Mopac 2002) and the self consistent reaction field(SCRF) model (implemented in Gaussian 98). Since the photo-physical properties of PM567 depend mainly on the solventpolarity and, to a lesser extent, on the solvent basicity,17 theconsidered solvents in the present work are: c-hexane as apolarsolvent (dielectric constant e ¼ 2.0), acetone as a polar/non-protic (e ¼ 20.7) solvent and methanol as a polar/protic(e ¼ 32.7) solvent. The optimization with the COSMO modelwas performed using the default options and considering asolvent radius of 2.52 A for methanol, 3.07 A for acetone and3.50 A for c-hexane21 and a solute cavity radius of 5.65 A,obtained from volume calculations for PM567 at the B3LYP/6-31G level. In the SCRFmethod, the solvent was simulated bythe Onsager and polarizable continuum model (PCM)theories,27,28 both implemented in the Gaussian 98 software,and the integral equation formalism PCM (IEF-PCM),29 areformulation of the latter theory incorporated in the Gaussian03 software. The 6-31G and 6-31þG* functions were used asbasis sets.

The photophysical characteristics were theoretically calcu-lated by the time-dependent DFT (TD-DFT) method30 (im-plemented in the Gaussian 03 software) applied to B3LYPgeometries, and by Zerner’s intermediate neglect of differentialoverlap (ZINDO)31 and configuration interaction singles anddoubles (CISD, up to 861 configurations) methods, both overPM5 geometries and considering ten molecular orbitals in theactive space.

Results and discussion

The geometrical parameters of the S0 ground state of thePM567 dye optimized by means of DFT and semiempiricalPM5 methods are listed in Table 1. The corresponding experi-mental data obtained from X-ray diffraction analysis are alsoincluded for comparison.32 PM567 does not crystallize in asymmetric cell, but the geometry of PM567 optimized by

several theoretical methods shows a symmetry plane betweenthe two pyrrole rings, and for this reason, the geometricalparameters theoretically obtained for symmetrical counter-parts are not included in Table 1. However, the observed slightdeviation from planarity located in the central ring linking thetwo pyrrole rings (dihedral angle C3–C4–C5–C6 ¼ 176.01 byB3LYP/6-31G geometry, Table 1) disrupts the C2v point groupfor PM567.We must point out the good correlation between the calcu-

lated bond lengths and angles (deviations not greater than0.03 A and 21) by the DFT method and experimental X-raydiffraction data. Moreover, the computationally not so-expen-sive semiempirical PM5 method also provides satisfactoryresults. However, the calculated dihedral angles show devia-tions from the experimental data. This discrepancy can beassigned to the packing forces in the crystalline state of PM567needed to obtain the experimental geometrical parameters.34,35

Indeed, theoretical calculations are obtained in the gas phasewithout any intermolecular interactions, whereas the packingforces could disrupt the planarity of the aromatic p-system ofPM567 in the solid state (non-symmetric crystalline cell). Themain differences between the calculated geometry by thesemiempirical PM5 level and by DFT methods (and betweenthe different basis sets in the DFT method) are located at theN2BF2 group (Table 1). This could be due to an underestima-tion of the electronic density in the N-atoms in the semiempi-rical method, as has been discussed elsewhere.20

The ground state geometry of PM567 is not very different tothat of PM546 (without ethyl groups at 2 and 6 positions).20

However, the presence of ethyl groups induces an increase inthe bond lengths involving the carbons of positions 2 and 6,which can be attributed to the inductive electron releasingcharacter of the ethyl substituents. Moreover, the presence ofthese ethyl substituents leads to a slight deviation from pla-narity of the two pyrrole rings (dihedral angle C1–C2–C3–C4

for PM567 of 0.61, in Table 1, versus that of 0.21 for PM54623

by PM5 method). This deviation should be assigned to a sterichindrance with the adjacent methyl groups at the 1 and 3, and 5and 7 positions, respectively, since a higher deviation from theplanarity (dihedral angle C1–C2–C3–C4 ¼ 3.61 for PM597 bythe semiempirical AM1 method) was observed with bulkyt-butyl groups.18

The presence of the ethyl group at the 2 and 6 positions ofthe PM chromophore also affects the charge distribution of thep-system. Fig. 2 shows the electronic density in the S0 groundstate of PM567 and the Mulliken point charges through thechromophore obtained by the DFT method. The chargedensity is symmetrically distributed in the p-system due tothe symmetry plane located at the molecule short axis. Nega-tive charge densities are localized in the nitrogen and fluorineatoms, while the carbon atoms carry a net positive chargedensity. Such a charge distribution leads to a dipole moment ofthe ground state of PM567 along the molecular short axis(Fig. 2). Probably, the more electronegative nitrogen andfluorine atoms take the negative charge density from the boronatom, as reported elsewhere.20 On the other hand, and due tothe inductive electron donor character of the ethyl group, theadjacent carbons at the 2 and 6 positions of the PM chromo-phore show a more negative charge density in PM567 (0.108)than in PM546 (0.119).20 The dipole moment of PM567 (m ¼4.93 D by B3LYP and m ¼ 5.06 D by PM5) slightly decreaseswith respect to that of PM546 (m ¼ 5.14 D and m ¼ 5.25 D,respectively).20

The geometry of PM567 has also been optimized consideringthe solvent effect by different SCRF methods (Onsager, PCMand IEF-PCM) and the COSMO algorithm, included in theDFT (B3LYP) and semiempirical PM5 levels, respectively.Table 2 lists the geometrical parameters of PM567 providedby the IEF-PCM and COSMO methods in c-hexane, acetoneand methanol (bond angles are not included since they do

Fig. 1 Molecular structures of PM546 and PM567.

4248 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 2 4 7 – 4 2 5 3 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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not change significantly). These solvents have been chosen dueto their different nature: c-hexane provides an apolar environ-ment; acetone is a polar/non-protic solvent; and methanol as apolar/protic solvent. The data obtained by the Onsager modelhave not been included in Table 2 because there was nosignificant effect of the solvent in the geometrical parametersof PM567. In the case of ab initio calculations, both PCM andIEF-PCM methods predict a similar geometry and are ana-lyzed as a whole.Some conclusions can be drawn from the data in Table 2. As

was expected, the geometrical parameters in c-hexane are closeto those obtained in the gas phase (Table 1). Moreover, bothPCM and COSMO establish an alternative lengthening(C1–N11, C2–C3 and their symmetrical bonds) and shrinking(C1–C2, C3–C4 and their symmetrical bonds) of the bondlengths through the chromophore p-system, going from apolar

Fig. 2 Electronic density of the ground state of PM567. The Mullikenpoint charges calculated with B3LYP/6-31G are also included. Corres-ponding symmetrical counterparts are not included.

Table 1 Bond lengths, angles and dihedral angles of the S0 ground state (calculated by B3LYP and PM5 methods) and S1 excited state (CIS

method)33 of PM567. The corresponding data for the symmetrical counterpart are not included. The experimental data obtained by X-ray

diffraction32 are also included for comparison

B3LYP/6-31G B3LYP/6-31 þ G* PM5 CIS/6-31G X-raya

Bond lengths (�0.001 A)

C1–C2 (C8–C9) 1.421 1.418 1.435 1.415 1.395 (1.393)

C2–C3 (C7–C8) 1.407 1.400 1.388 1.392 1.380 (1.399)

C3–C4 (C6–C7) 1.438 1.435 1.440 1.431 1.425 (1.415)

C4–C5 (C5–C6) 1.409 1.409 1.393 1.410 1.399 (1.407)

C1–N11 (C9–N10) 1.359 1.348 1.354 1.344 1.345 (1.347)

C4–N11 (C6–N10) 1.409 1.398 1.425 1.405 1.396 (1.401)

N11–B12 (N10–B12) 1.537 1.551 1.584 1.524 1.527 (1.550)

F13–B12 (F14–B12) 1.440 1.406 1.378 1.436 1.377 (1.397)

Bond angles (�0.11)

C1–C2–C3 (C9–C8–C7) 107.5 107.2 107.7 107.7 106.9 (107.0)

C2–C3–C4 (C8–C7–C6) 107.1 106.8 107.6 107.0 106.9 (107.5)

C3–C4–C5 (C7–C6–C5) 132.6 132.1 132.1 132.1 133.7 (134.2)

C4–C5–C6 120.5 120.7 121.3 118.4 121.9

C1–N11–C4 (C9–N10–C6) 109.2 108.9 109.0 109.3 108.5 (108.8)

C2–C1–N11 (C8–C9–N10) 109.0 109.5 108.9 109.0 110.0 (109.7)

C3–C4–N11 (C7–C6–N10) 106.9 107.4 106.5 106.8 106.4 (106.8)

C5–C4–N11 (C5–C6–N10) 120.3 120.4 121.2 121.0 119.8 (119.0)

B12–N11–C4 (B12–N10–C6) 125.6 125.5 124.0 125.4 126.3 (126.2)

B12–N11–C1 (B12–N10–C9) 125.0 125.5 126.7 125.1 125.0 (125.0)

N10–B12–N11 107.4 106.8 106.7 107.3 106.7

Dihedral angles (�0.11)

C1–C2–C3–C4 (C6–C7–C8–C9) 0.2 0.2 �0.6 1.0 0.8 (1.4)

C2–C3–C4–C5 (C5–C6–C7–C8) 179.6 179.1 �178.8 177.8 178.2 (178.9)

C3–C4–C5–C6 (C4–C5–C6–C7) 176.0 174.3 168.8 169.6 177.6 (177.7)

C3–C4–N11–C1 (C7–C6–N10–C9) 0.7 0.8 1.9 1.8 1.7 (0.5)

C3–C2–C1–N11 (C7–C8–C9–N10) 0.4 0.6 1.1 0.1 1.8 (1.7)

C5–C4–N11–C1 (C5–C6–N10–C9) �179.9 �179.7 179.0 �177.8 �179.6 (�179.7)

C2–C3–C4–N11 (C8–C7–C6–N10) 0.4 0.6 1.2 1.6 0.5 (0.6)

C4–N11–C1–C2 (C6–N10–C9–C8) 0.7 0.9 1.9 1.1 2.3 (1.4)

C4–C5–C6–N10 (C6–C5–C4–N11) 3.2 4.2 9.5 10.8 1.7 (0.8)

C2–C1–N11–B12 (C8–C9–N10–B12) 179.6 178.9 179.1 179.4 176.7 (176.3)

C3–C4–N11–B12 (C7–C6–N10–B12) �179.7 �178.8 179.0 �178.7 177.2 (177.1)

C5–C4–N11–B12 (C5–C6–N10–B12) 0.4 2.2 0.3 1.6 1.9 (2.4)

C6–N10–B12–N11 (C4–N11–B12–N10) 3.4 7.1 8.4 6.6 �2.2 (2.4)

C1–N11–B12–N10 (C9–N10–B12–N11) 177.1 175.0 172.8 174.1 179.0 (178.7)

a Average value of the two geometries provided by X-ray diffraction data.

P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 2 4 7 – 4 2 5 3 4249T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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to polar solvents. Indeed, the bond length alternation (BLA)parameter,36 defined as the difference between the carbon-carbon single and double in the polymethine backbone, as itis the case of PM dyes, accounts for the statistical weight of theresonance structures with the longest and the shortest chargeseparation. Thus, the BLA parameter decreases in polar sol-vents (from 0.020 in c-hexane to 0.016 in methanol by PCMmethods). Considering the resonance structures of the PMchromophore depicted in Fig. 3, a lower BLA value wouldbe ascribed to a higher statistical weight of the resonancestructure ‘‘d’’ with the highest charge density separation. Thiscanonical form has the positive charge in the C5 atom and thenitrogen atoms with a sp3 hybridation. Besides, the dihedralangles show a general tendency of a slight lower planarity ofPM567 in methanol, confirming the higher statistical weight ofthe resonance structure ‘‘d’’ in polar solvents. Moreover, inprevious works for PM dyes,16,17 it was concluded that theresonance structure ‘‘d’’ has a higher statistical weight in theground S0 state than in the excited S1 state owing to the morepolar character of the former state. Thus, polar solvents wouldstabilize this structure more extensively and hence the groundstate, leading to an increase in the energy gap between bothstates. This hypsochromic shift is discussed in more detail below.

On the other hand, it has to be pointed out that the bondlengths involving the linkage group (BF2) between the twopyrrole units change with the solvent nature (Table 2). Thistrend may be related to the higher electronic density in theN2BF2 group (Fig. 2). In order to elucidate this aspect, thesolvent effect on the electronic charge distribution is analyzed.Table 3 lists the charge distribution of the S0 ground state of

PM567 obtained by Mulliken and by the more accurate Chelpgmethods in c-hexane and methanol, the latter fits the charges tothe electrostatic potential. The differences between the Mulli-ken charges obtained with DFT and semiempirical methodsare attributed to the tendency of the latter calculation tounderestimate the electronegativity the nitrogen atoms. Inagreement with the geometries discussed above, the chargedistribution obtained in c-hexane is very close to that in the gasphase. However, a slight augmentation in the negative electro-nic density in the B and N atoms together with an increase inthe positive electronic density at the central C5 atom isobserved by both PCM methods and the COSMO algorithmin methanol (Table 2). Such a charge distribution in the polarsolvent along the short molecular axis supports the abovementioned higher statistical weight of the resonance structure‘‘d’’, which has the highest charge separation. Thus, a higherdipole moment of PM567 is expected in polar solvents, as isreflected in the calculated value (Table 3). We must point outthe excellent agreement in the dipole moment calculated by theDFT-PCM and PM5-COSMO methods. The Onsager methodalso reproduces this trend, although the charge density issimilar in both solvents.From the optimized geometry of the S0 ground state in the

three solvents, the absorption spectra have been calculated byassuming Franck–Condon transitions in order to elucidate thesolvent effect on the absorption characteristics of PM567. Theabsorption simulation has been performed by the TD-DFTmethod and semiempirical ZINDO over PCM and IEF-PCMgeometries, and semiempirical ZINDO and CISD/PM5 overCOSMO geometries. It was previously characterized that the

Table 2 Optimized bond distances and dihedral angles of the S0 ground state if PM567 in c-hexane, acetone and methanol obtained by the IEF-

PCM model at the B3LYP/6-31G level and the COSMO algorithm at the semiempirical PM5 level. Atoms labels are those of Table 1. The

corresponding counterparts data are not included

IEF-PCM/B3LYP/6-31G COSMO/PM5

C-hexane Acetone Methanol C-hexane Acetone Methanol

Bond lengths (�0.001A)

C1–C2 1.419 1.418 1.417 1.435 1.432 1.430

C2–C3 1.407 1.409 1.410 1.389 1.391 1.392

C3–C4 1.438 1.436 1.436 1.440 1.439 1.438

C4–C5 1.409 1.410 1.410 1.393 1.395 1.395

C1–N11 1.361 1.364 1.365 1.355 1.358 1.359

C4–N11 1.411 1.413 1.413 1.425 1.428 1.428

N11–B12 1.535 1.530 1.529 1.581 1.574 1.573

F13–B12 1.443 1.450 1.450 1.381 1.386 1.388

Dihedral angles (�0.11)

C1–C2–C3–C4 0.2 0.2 0.2 �0.7 �0.8 �0.8

C2–C3–C4–C5 179.7 179.5 179.5 �178.6 �178.9 �178.7

C3–C4–C5–C6 175.8 175.7 175.3 168.3 168.5 168.3

C3–C4–N11–C1 0.7 0.7 0.8 1.7 1.8 1.9

C3–C2–C1–N11 0.4 0.3 0.4 1.1 1.1 1.1

C5–C4–N11–C1 179.9 �179.8 179.9 178.9 179.2 179.1

C2–C3–C4–N11 0.5 0.5 0.5 0.9 1.2 1.2

C4–N11–C1–C2 0.7 0.7 0.6 1.8 1.8 1.9

C4–C5–C6–N10 3.2 3.2 3.6 9.6 9.4 9.3

C2–C1–N11–B12 179.7 179.6 179.7 179.4 179.3 179.4

C3–C4–N11–B12 179.6 179.5 179.4 179.6 179.4 179.6

C5–C4–N11–B12 0.4 0.5 0.7 1.2 1.0 1.0

C6–N10–B12–N11 3.4 3.6 3.9 10.0 9.2 9.6

C1–N11–B12–N10 177.1 176.9 176.6 171.5 172.2 172.0

Fig. 3 Resonance structures of PM-chromophore.

4250 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 2 4 7 – 4 2 5 3 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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S0–S1 transition of PM dyes is a promotion of one electronfrom the HOMO to the LUMO state and it is polarized alongthe long molecular axis, perpendicular to the molecular dipolemoment.20,33,37 Fig. 4(A and B) shows the contour maps ofthese frontier orbitals. The transition density can be calculatedby multiplying the electronic density of the involved HOMOand LUMO states.38 The transition density of PM567 is shownin Fig. 4(D). High transition density is localized in the pyrrolerings, indicating that the transition is polarized along themolecular long axis, C1 and its symmetrical counterpart C9

atoms contributing most to the electronic transition.Table 4 summarizes the calculated absorption and fluores-

cence properties in the three solvents. The correspondingexperimental data are also included. All the methods over-estimate the absorption energy gap; however, semiempiricalZINDO and CISD methods provide satisfactory DEab valueswith respect to those experimentally obtained (differences lessthan 0.2 eV). Moreover, the TD method supplied an oscillatorstrength (f) value close to the experimental value, although thesemiempirical methods overestimate this value. From theseresults it is concluded that semiempirical and DFT methodsprovide complementary results in the absorption characteris-tics of PM dyes, as was also concluded from the theoreticalcalculations of PM546.20

The absorption energy gap and oscillator strength inc-hexane are nearly the same to those in the gas phase due tothe inert nature of this solvent (Table 4). In polar solvents theabsorption energy gap slightly increases with respect toc-hexane (around 0.02 eV) in all the used methods, except inthe ZINDO method, which is 0.05 eV (Table 4). These theore-tical results correlate with the experimentally observed hypso-chromic shift (around 0.03 eV) changing the solvent from

apolar to polar/protic solvents.17 Moreover, the experimentallyobserved diminution of the oscillator strength (f) in polarsolvents is also proposed by all the theoretical methods usedin the present work. The hypsochromic shift is a consequenceof the decrease in the molecule dipole moment along the shortaxis upon excitation.The dipole moment in the excited Franck–Condon S1 state

has been evaluated by the semiempirical CISD and ZINDOmethods. Both methods predict a diminution in the dipolemoment (Dm ¼ 1.08 D by CISD and Dm ¼ 1.96 D by ZINDOmethods) upon excitation either in c-hexane or in acetone andmethanol. Indeed, the difference in the electronic densitybetween the LUMO and HOMO states, which is illustratedin Fig. 4c, shows an alternating distribution through thep-system, suggesting a small change in the dipole momentand therefore a low solvent dependence on the absorptionband.37

The fluorescence properties of PM567 were also theoreticallycalculated from the optimized geometry of the S1 state by theCIS method,33 using the TD-DFT method. Due to the highcomputational cost of the optimization in the excited state, thesolvent effect on the fluorescence properties of PM567 wassimulated by PCM and IEF-PCM models from geometryoptimized in the S1 excited state in the gas phase. The solventwas not considered in this optimization procedure. Indeed, thesolvent does not induce drastic changes in the geometry of theS0 ground state of PM567, as is discussed above. Moreover,the geometry of PM567 in both S0 and S1 states is similar. As isshown by absorption data, both PCM models overestimate theenergy gap of the emission transition with respect to theexperimental value (Table 4), although the value calculatedby the IEF-PCM method is closer to the experimental one.Both levels, however, adequately predict the evolution of DEfl

with the solvent. Similar arguments to those used to explain thesolvatochromic effect in the absorption band can be alsoapplied to explain the hypsochromic shift of the fluorescenceband with solvent polarity. The corresponding small Stokesshift is consistent with the small modification in the geometryof PM567 in both S0 and S1 states. Theoretical results do notadequately predict the solvent effect in the Stokes shift,although the small differences could be within the computa-tional errors.The transition moment probability between S1 - S0 states

can be discussed from fluorescence data on the basis of theradiative deactivation rate constant kfl parameter. The kfl valuecan be evaluated from the S1 - S0 oscillator strength (f) bymeans of:39

kfl ¼ A ¼ 2pn2e2

c3mee0f ð1Þ

where A is the Einstein spontaneous emission coefficient, n isthe calculated emission wavenumber, e and me are the electroncharge and mass, respectively, c is the light speed, and e0 is the

Table 3 Charge distribution at the S0 ground state of PM567 chromophore in c-hexane and methanol obtained by DFT-PCM and PM5-COSMO

Mulliken and DFT-PCM Chelpg. The molecule dipole moment (in Debye) is also enclosed

C-hexane Methanol

Mulliken PCM Chelpg PCM Mulliken COSMO Mulliken PCM Chelpg PCM Mulliken COSMO

C1 0.348 0.326 0.167 0.341 0.323 0.167

C2 �0.026 �0.270 �0.049 �0.027 �0.271 �0.049

C3 0.108 0.087 0.005 0.107 0.066 0.007

C4 0.142 �0.010 0.038 0.137 �0.034 0.039

C5 0.182 0.157 0.089 0.193 0.159 0.095

N10 �0.759 �0.379 �0.324 �0.765 �0.396 �0.328

B12 0.924 0.884 0.928 0.906 0.880 0.923

F13 �0.398 �0.463 �0.525 �0.415 �0.477 �0.528

Dipole 5.5 5.6 5.7 6.9 7.0 7.3

Fig. 4 Electronic contour maps of the HOMO (A) and LUMO (B)states obtained by B3LYP calculation. The differential electronicdensity of the HOMO and LUMO states (C) and the transition densitycalculated by the ZINDO method (D) are also included.

P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 2 4 7 – 4 2 5 3 4251T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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vacuum dielectric constant. Similar to that predicted by ab-sorption data through the f values, the theoretically calculatedkfl value suggests a decrease in the S1 - S0 transition prob-ability by increasing the solvent polarity (Table 4). However,an opposite evolution of the kfl value with the solvent isexperimentally observed (Table 4). Probably, the non-consid-eration of the solvent in the geometry optimization of the S1state could lead to a less adequate evaluation of the kflparameter. Moreover, in spite of the differences observed inthese solvents, it was experimentally concluded for a multitudeof nonpolar, polar and protic solvents that the kfl value ofPM567 is nearly solvent independent.17 To sum up, the use ofthe present quantum mechanic calculations suggests the com-plementarity of semiempirical and DFT methods, since theformer provide more accurate values for the transition energygap, whereas the latter reproduce adequately the experimentalsolvent evolution of the transition energy and oscillatorstrength.

Theoretical calculations do not provide the non-radiativedeactivation rate constant (knr) and hence the value of thefluorescence quantum yield (ffl), but it could be qualitativelyestimated from the proposed mechanisms for the non-radiativedeactivation processes. Since the intersystem crossing prob-ability in PM dyes is very low,6,7 knr is mainly due to internalconversion processes, which are related to the flexibility/rigid-ity of the dye2,19,40 and to the electron flow through thechromophoric p-system.40 Theoretical calculations suggest thatthe presence of ethyl groups at the 2 and 6 positions of PM567reduce the planarity of the pyrrole groups. Consequently, it istheoretically predicted that the fluorescence quantum yieldshould have lower values than those of PM546, as is experi-mentally observed.16 Moreover, the presence of bulky t-butylgroups at these positions increases the deviation from theplanarity of the pyrrole groups, explaining the important lossesin the fluorescence efficiency of PM597 dye.18 On the otherhand, the increase of the fluorescence quantum yield of PM567in polar/protic solvents17 cannot exclusively attributed to theeffect of the solvent on the planarity of the chromophore.Indeed polar solvents would stabilize the non-planar resonancestructure ‘‘d’’ in Fig. 3 and a decrease in the fluorescencequantum yield should be expected in polar solvents. However,since protic solvents would interact with the positive chargeand the electron lone-pair of the N-atoms of the PM chromo-phoric system, these specific interactions would reduce theelectron flow through the p-system40 decreasing the internalconversion of PM567 in polar/protic solvents.17

Conclusions

Quantum mechanical calculations at the DFT and semiempi-rical levels are powerful tools to study the photophysicalproperties of PM dyes. The presence of ethyl groups at the 2and 6 positions of the chromophore slightly disrupts theplanarity of the two pyrrole rings. Ab initio SCRF andsemiempirical COSMO methods are used and proved to beadequate models to evaluate the solvent effect on the photo-physical properties of PM567. The preferential solvation ofthe different resonance structures can be used to explain theevolution of the photophysical properties of PM567 with thesolvent. Theoretical data in c-hexane are close to those inthe gas phase, as is expected for the inert character of this solvent.However, polar solvents favor that resonance structure withthe highest dipole moment, which is also characterized by a sp3

hybridation of the nitrogen atoms. This resonance structurereduces the absorption probability in polar solvents, as isexperimentally confirmed. All theoretical methods, and mainlythe TD-DFT method, suggest a hypsochromic shift in bothabsorption and fluorescence bands and a diminution in theoscillator strength in polar solvents. However, semiempiricalmethods provide more accurate transition energies, suggestingthe complementarity of semiempirical and DFT methods topredict the photophysics of PM dyes.

Acknowledgements

This work was supported by the Spanish minister (MAT2000-1361-C04-02) project. J. B. P. and V. M. M. thank the UPV/EHU and MECD for their research grants. Dr L. Carretero isthanked for the optimization of the excited state geometry ofPM567, and Dr B. Herradon is also thanked for X-raydiffraction data.

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P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 2 4 7 – 4 2 5 3 4253T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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